Synchronization and Basins of Synchronized in Two-Dimensional Piecewise Maps Via Coupling Three Pieces of One-Dimensional Maps

This paper is devoted to the synchronization of a dynamical system defined by two different coupling versions of two identical piecewise linear bimodal maps. We consider both local and global studies, using different tools as natural transversal Lyapunov exponent, Lyapunov functions, eigenvalues and eigenvectors and numerical simulations. We obtain theoretical results for the existence of synchronization on coupling parameter range. We characterize the synchronization manifold as an attractor and measure the synchronization speed. In one coupling version, we give a necessary and sufficient condition for the synchronization. We study the basins of synchronization and show that, depending upon the type of coupling, they can have very different shapes and are not necessarily constituted by the whole phase space; in some cases, they can be riddled.

Travelling to India: Eliza Fay’s narrative account of her voyages

Eliza Fay’s Original Letters from India (1817), initially sold to the Calcutta Gazette to pay off her debts, aroused the curiosity and interest of Edward M. Forster, while he was doing research for his best-selling novel, A Passage to India. In his own words, “Eliza Fay is a work of art.” (apud Fay 7) The value of E. Fay’s travelogue, comprising not one, but three voyages to India (in 1779, 1784, 1796) can be easily explained if we take into account the scope of its geographical coverage, the hardships of its historical context (the political chaos brought about by the fall of the Mughal empire and the consolidation of the British rule in the Indian subcontinent) and the heroism of the first person-narrator that emerges behind the descriptive sketches and the scenes of adversity and imminent danger. Thus the current analysis will focus on the E. Fay’s adventurous mode of narrating, e.g., the discursive situatedness of the traveller visà- vis the Other(s) (European and non-European peoples and loci) and the constraints imposed by the patriarchal idealization of the domestic Woman and their alleged feebleness.

East of Suez and the imaginary tangles of space and self

Drawing on postcolonial studies and the theorization on imperial gothic, this paper centres on three texts: The Hosts of the Lord (1900) by Flora Annie Steel; East of Suez (1901) by Alice Perrin, and The Way of an Eagle (1912)by Ethel Dell. These three texts highlight in different ways the discursive mediation of the Other and its destabilizing effects on the identity of the European-minded colonizer, thus foregrounding the multifarious nature of the British imaginative engagement with India. In this context, it is particularly relevant to examine the political and ideological implications of representing anywhere East of Suez as a locus of primitivism and chaos vis-à-vis the colonizer’s ambivalent reactions. Thus we seek to demonstrate the power of two distinct practices or modes of representation – namely, the power of a metaphorical discourse versus metonymic discourse- within the proces of constructing the East for a vast Western readership.

The 1998 Faial earthquake, Azores: Evidence for a transform fault associated with the Nubia-Eurasia plate boundary?

With very few exceptions, M > 4 tectonic earthquakes in the Azores show normal fault solution and occur away from the islands. Exceptionally, the 1998 shock was pure strike-slip and occurred within the northern edge of the Pico-Faial Ridge. Fault plane solutions show two possible planes of rupture striking ENE-WSW (dextral) and NNW-SSE (sinistral). The former has not been recognised in the Azores, but is parallel to the transform direction related to the relative motion between the Eurasia and Nubia plates. Therefore, the main question we address in the present study is: do transform faults related to the Eurasia/Nubia plate boundary exist in the Azores? Knowing that the main source of strain is related to plate kinematics, we conclude that the sinistral strike-slip NNW-SSE fault plane solution is not consistent with either the fault dip (ca. 65, which is typical of a normal fault) or the ca. ENE-WSW direction of maximum extension; both are consistent with a normal fault, as observed in most major earthquakes on faults striking around NNW-SSE in the Azores. In contrast, the dextral strike-slip ENE-WSW fault plane solution is consistent with the transform direction related to the anticlockwise rotation of Nubia relative to Eurasia. Altogether, tectonic data, measured ground motion, observed destruction, and modelling are consistent with a dextral strike-slip source fault striking ENE-WSW. Furthermore, the bulk clockwise rotation measured by GPS is typical of bookshelf block rotations observed at the termination of such master strike-slip faults. Therefore, we suggest that the 1998 earthquake can be related to the WSW termination of a transform (ENE-WSW fault plane solution) associated with the Nubia-Eurasia diffuse plate boundary. (C) 2014 Elsevier B.V. All rights reserved.

Avoiding healthy cells extinction in a cancer model

We consider a dynamical model of cancer growth including three interacting cell populations of tumor cells, healthy host cells and immune effector cells. For certain parameter choice, the dynamical system displays chaotic motion and by decreasing the response of the immune system to the tumor cells, a boundary crisis leading to transient chaotic dynamics is observed. This means that the system behaves chaotically for a finite amount of time until the unavoidable extinction of the healthy and immune cell populations occurs. Our main goal here is to apply a control method to avoid extinction. For that purpose, we apply the partial control method, which aims to control transient chaotic dynamics in the presence of external disturbances. As a result, we have succeeded to avoid the uncontrolled growth of tumor cells and the extinction of healthy tissue. The possibility of using this method compared to the frequently used therapies is discussed. (C) 2014 Elsevier Ltd. All rights reserved.

Topological entropy of catalytic sets: Hypercycles revisited

The dynamics of catalytic networks have been widely studied over the last decades because of their implications in several fields like prebiotic evolution, virology, neural networks, immunology or ecology. One of the most studied mathematical bodies for catalytic networks was initially formulated in the context of prebiotic evolution, by means of the hypercycle theory. The hypercycle is a set of self-replicating species able to catalyze other replicator species within a cyclic architecture. Hypercyclic organization might arise from a quasispecies as a way to increase the informational containt surpassing the so-called error threshold. The catalytic coupling between replicators makes all the species to behave like a single and coherent evolutionary multimolecular unit. The inherent nonlinearities of catalytic interactions are responsible for the emergence of several types of dynamics, among them, chaos. In this article we begin with a brief review of the hypercycle theory focusing on its evolutionary implications as well as on different dynamics associated to different types of small catalytic networks. Then we study the properties of chaotic hypercycles with error-prone replication with symbolic dynamics theory, characterizing, by means of the theory of topological Markov chains, the topological entropy and the periods of the orbits of unimodal-like iterated maps obtained from the strange attractor. We will focus our study on some key parameters responsible for the structure of the catalytic network: mutation rates, autocatalytic and cross-catalytic interactions.

Complex Dynamics of defective interfering baculoviruses during serial passage in insect cells

Defective interfering (DI) viruses are thought to cause oscillations in virus levels, known as the ‘Von Magnus effect’. Interference by DI viruses has been proposed to underlie these dynamics, although experimental tests of this idea have not been forthcoming. For the baculoviruses, insect viruses commonly used for the expression of heterologous proteins in insect cells, the molecular mechanisms underlying DI generation have been investigated. However, the dynamics of baculovirus populations harboring DIs have not been studied in detail. In order to address this issue, we used quantitative real-time PCR to determine the levels of helper and DI viruses during 50 serial passages of Autographa californica multiple nucleopolyhedrovirus (AcMNPV) in Sf21 cells. Unexpectedly, the helper and DI viruses changed levels largely in phase, and oscillations were highly irregular, suggesting the presence of chaos. We therefore developed a simple mathematical model of baculovirus-DI dynamics. This theoretical model reproduced patterns qualitatively similar to the experimental data. Although we cannot exclude that experimental variation (noise) plays an important role in generating the observed patterns, the presence of chaos in the model dynamics was confirmed with the computation of the maximal Lyapunov exponent, and a Ruelle-Takens-Newhouse route to chaos was identified at decreasing production of DI viruses, using mutation as a control parameter. Our results contribute to a better understanding of the dynamics of DI baculoviruses, and suggest that changes in virus levels over passages may exhibit chaos.

N’A Barraca com Maria do Céu Guerra em Dona Maria, a louca, de António Cunha: relatório de estágio

Relatório de Estágio submetido à Escola Superior de Teatro e Cinema para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Teatro - especialização em Artes Performativas - Interpretação.

Conversas de palco: relatório de estágio

Relatório de Estágio submetido à Escola Superior de Teatro e Cinema para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Teatro - especialização em Design de Cena.

Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach

In this article we provide homotopy solutions of a cancer nonlinear model describing the dynamics of tumor cells in interaction with healthy and effector immune cells. We apply a semi-analytic technique for solving strongly nonlinear systems – the Step Homotopy Analysis Method (SHAM). This algorithm, based on a modification of the standard homotopy analysis method (HAM), allows to obtain a one-parameter family of explicit series solutions. By using the homotopy solutions, we first investigate the dynamical effect of the activation of the effector immune cells in the deterministic dynamics, showing that an increased activation makes the system to enter into chaotic dynamics via a period-doubling bifurcation scenario. Then, by adding demographic stochasticity into the homotopy solutions, we show, as a difference from the deterministic dynamics, that an increased activation of the immune cells facilitates cancer clearance involving tumor cells extinction and healthy cells persistence. Our results highlight the importance of therapies activating the effector immune cells at early stages of cancer progression.

Explicit series solution for a glucose-induced electrical activity model of pancreatic beta-cells

In this work, we present the explicit series solution of a specific mathematical model from the literature, the Deng bursting model, that mimics the glucose-induced electrical activity of pancreatic beta-cells (Deng, 1993). To serve to this purpose, we use a technique developed to find analytic approximate solutions for strongly nonlinear problems. This analytical algorithm involves an auxiliary parameter which provides us with an efficient way to ensure the rapid and accurate convergence to the exact solution of the bursting model. By using the homotopy solution, we investigate the dynamical effect of a biologically meaningful bifurcation parameter rho, which increases with the glucose concentration. Our analytical results are found to be in excellent agreement with the numerical ones. This work provides an illustration of how our understanding of biophysically motivated models can be directly enhanced by the application of a newly analytic method.

On the analytical solutions of the Hindmarsh-Rose neuronal model

In this article we analytically solve the Hindmarsh-Rose model (Proc R Soc Lond B221:87-102, 1984) by means of a technique developed for strongly nonlinear problems-the step homotopy analysis method. This analytical algorithm, based on a modification of the standard homotopy analysis method, allows us to obtain a one-parameter family of explicit series solutions for the studied neuronal model. The Hindmarsh-Rose system represents a paradigmatic example of models developed to qualitatively reproduce the electrical activity of cell membranes. By using the homotopy solutions, we investigate the dynamical effect of two chosen biologically meaningful bifurcation parameters: the injected current I and the parameter r, representing the ratio of time scales between spiking (fast dynamics) and resting (slow dynamics). The auxiliary parameter involved in the analytical method provides us with an elegant way to ensure convergent series solutions of the neuronal model. Our analytical results are found to be in excellent agreement with the numerical simulations.

Nonautonomous Graphs and Topological Entropy of Nonautonomous Lorenz Systems

In this work, we associate a p-periodic nonautonomous graph to each p-periodic nonautonomous Lorenz system with finite critical orbits. We develop Perron-Frobenius theory for nonautonomous graphs and use it to calculate their entropy. Finally, we prove that the topological entropy of a p-periodic nonautonomous Lorenz system is equal to the entropy of its associated nonautonomous graph.